From microstructural features to effective toughness in disordered brittle solids

Abstract

The relevant parameters at the microstructure scale that govern the macroscopic toughness of disordered brittle materials are investigated theoretically. We focus on planar crack propagation and describe the front evolution as the propagation of a long-range elastic line within a plane with random distribution of toughness. Our study reveals two regimes: in the collective pinning regime, the macroscopic toughness can be expressed as a function of a few parameters only, namely the average and the standard deviation of the local toughness distribution and the correlation lengths of the heterogeneous toughness field; in the individual pinning regime, the passage from micro to macroscale is more subtle and the full distribution of local toughness is required to be predictive. Beyond the failure of brittle solids, our findings illustrate the complex filtering process of microscale quantities towards the larger scales into play in a broad range of systems governed by the propagation of an elastic interface in a disordered medium.

7 pages, 4 figures

References in corpus (7)

• Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
• Width distribution of contact lines on a disordered substrate
• Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition
• Thermal rounding of the depinning transition
• Fracturing highly disordered materials
• Quantitative prediction of effective toughness at random heterogeneous interfaces
• Universality Classes in Constrained Crack Growth

Cited by in corpus (14)

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• An FFT-based method for computing the effective crack energy of a heterogeneous material on a combinatorially consistent grid
• Localization of soft modes at the depinning transition
• Crack-front model for adhesion of soft elastic spheres with chemical heterogeneity
• Universal scaling of the velocity field in crack front propagation
• Size effects in the toughening of brittle materials by heterogeneities: a non-linear analysis of front deformations
• Quasi-static crack front deformations in cohesive materials
• A comprehensive study of nonlinear perturbations in the dynamics of planar crack fronts
• Loss of memory of an elastic line on its way to limit cycles
• Dynamic crack growth along heterogeneous planar interfaces: interaction with unidimensional strips
• Dual Role for Heterogeneity in Dynamic Fracture
• Pinning by rare defects and effective mobility for elastic interfaces in high dimensions
• Pinning-depinning transitions in two classes of discrete elastic-string models in (2+1)-dimensions